In these previous works, the fluctuations have been introduced in the viscosity as inspired by magneto-hydrodynamic simulations [1]}. However, in the standard \(\alpha \) -disc model [2]}, the viscosity is parametrised by \(\alpha \)  such that the viscous stress is \(\alpha P\) , where \(P\)  is the pressure. Viscous variations can be then represented by variation in the \(\alpha \)  parameter. Such simulations have been undertaken for, e.g., to study the effect of these variations on unstable radiation pressure dominated discs [3]} and to understand the effect of X-ray irradiation on the time dependent properties of the outer regions of an accretion disc [4]}. Since the nature especially the time-dependent behaviour of the turbulent viscosity is largely unknown, it is prudent to test different mechanisms by which the viscosity may fluctuate.
